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                <h2 id="引言："><a href="#引言：" class="headerlink" title="引言："></a>引言：</h2><blockquote>
<p>目标检测中的AP和mAP计算方法,看了几篇相关资料，知乎上一篇文章<br><a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/43068926">https://zhuanlan.zhihu.com/p/43068926</a> 写的容易理解，转载以学习，为了方便自己理解。</p>
</blockquote>
<h3 id="1、Recall-amp-Precision"><a href="#1、Recall-amp-Precision" class="headerlink" title="1、Recall &amp; Precision"></a>1、Recall &amp; Precision</h3><p>  mAP全称是mean Average Precision，这里的Average Precision，是在不同recall下计算得到的，所以要知道什么是mAP，要先了解recall（召回率）和precision（精确率）。<br>  recall和precision是二分类问题中常用的评价指标，通常以关注的类为正类，其他类为负类，分类器的结果在测试数据上有4种情况：</p>
<table>
<thead>
<tr>
<th></th>
<th>实际 1</th>
<th>实际 0</th>
</tr>
</thead>
<tbody><tr>
<td><strong>预测 1</strong></td>
<td>TP（True Positive）</td>
<td>FP（False Positive）</td>
</tr>
<tr>
<td><strong>预测 0</strong></td>
<td>FN（False Negative）</td>
<td>TN（True Negative）</td>
</tr>
</tbody></table>
<p>计算公式分别为：<br><img src="/posts/9fc5d2ad/1.png" alt="image"><br><strong>用一个具体的例子说明：</strong><br>  假设我们在数据集上训练了一个识别猫咪的模型，测试集包含100个样本，其中猫咪60张，另外40张为小狗。测试结果显示为猫咪的一共有52张图片，其中确实为猫咪的共50张，也就是有10张猫咪没有被模型检测出来，而且在检测结果中有2张为误检。因为猫咪更可爱，我们更关注猫咪的检测情况，所以这里将猫咪认为是正类：</p>
<p>所以TP&#x3D;50，TN&#x3D;38，FN&#x3D;10，FP&#x3D;2，P&#x3D;50&#x2F;52，R&#x3D;50&#x2F;60，acc&#x3D;(50+38)&#x2F;(50+38+10+2)</p>
<p><strong>为什么要引入recall和precision？</strong></p>
<p>recall和precision是模型性能两个不同维度的度量：</p>
<p>  在图像分类任务中，虽然很多时候考察的是accuracy，比如ImageNet的评价标准。但具体到单个类别，如果recall比较高，但precision较低，比如大部分的汽车都被识别出来了，但把很多卡车也误识别为了汽车，这时候对应一个原因。如果recall较低，precision较高，比如检测出的飞机结果很准确，但是有很多的飞机没有被识别出来，这时候又有一个原因。</p>
<p>  recall度量的是「查全率」，所有的正样本是不是都被检测出来了。比如在肿瘤预测场景中，要求模型有更高的recall，不能放过每一个肿瘤。</p>
<p>  precision度量的是「查准率」，在所有检测出的正样本中是不是实际都为正样本。比如在垃圾邮件判断等场景中，要求有更高的precision，确保放到回收站的都是垃圾邮件。</p>
<h3 id="2、mAP（mean-Average-Precision）"><a href="#2、mAP（mean-Average-Precision）" class="headerlink" title="2、mAP（mean Average Precision）"></a>2、mAP（mean Average Precision）</h3><p>在查找资料的过程中，发现从信息检索的角度出发更容易理解mAP的含义。</p>
<p>  在信息检索当中，比如我们搜索一个条目，相关的条目在数据库中一共有5条，但搜索的结果一共有10条（包含4条相关条目）。这个时候精确率precision&#x3D;返回结果中相关的条目数&#x2F;返回总条目数，在这里等于4&#x2F;10。召回率recall&#x3D;返回结果中相关条目数&#x2F;相关条目总数，在这里等于4&#x2F;5。但对于一个搜索系统，相关条目在结果中的顺序是非常影响用户体验的，我们希望相关的结果越靠前越好。比如在这个例子中，4个条目出现在位置查询一（1，2，4，7）就比在查询二（3，5，6，8）效果要好，但两者的precision是相等的。这时候单单一个precision不足以衡量系统的好坏，于是引入了AP（Average Precision）——不同召回率上的平均precision。对于上面两个例子。</p>
<p>查询一：</p>
<pre class="language-text" data-language="text"><code class="language-text">rank | correct |   P   |   R
-----------------------------
  1   | right  |  1/1  |  1/5
-----------------------------
  2  |  right  | 2/2  |  2/5
-----------------------------
  3  |  wrong  | 2/3  |  2/5
-----------------------------
  4  |   right | 3/4  |  3/5
-----------------------------
  5  |  wrong  | 3/5  |  3/5
-----------------------------
  6  |  wrong  | 3/6  |  3/5
-----------------------------
  7  |  right  | 4/7  |  4/5
-----------------------------
  8  |  wrong  | 4/8  |  4/5
-----------------------------
  9  |  wrong  | 4/9  |  4/5
-----------------------------
  10 |  wrong  | 4/10 |  4/5
------------------------------</code></pre>

<p>查询一：</p>
<pre class="language-text" data-language="text"><code class="language-text">rank | correct |   P   |   R
 -----------------------------
   1  |  wrong  |   0   |   0
 -----------------------------
   2  |  wrong  |   0   |   0
 -----------------------------
   3  |  right  | 1/3  |  1/5
 -----------------------------
   4  |  wrong  | 1/4  |  1/5
 -----------------------------
   5  |  right  | 2/5  |  2/5
 -----------------------------
   6  |  right  | 3/6  |  3/5
 -----------------------------
   7  |  wrong  | 3/7  |  3/5
 -----------------------------
   8  |  right  | 4/8  |  4/5
 -----------------------------
   9  |  wrong  | 4/9  |  4/5
 -----------------------------
  10  |  wrong  | 4/10 |  4/5
 -----------------------------</code></pre>

<p>AP(查询一) &#x3D; (1+1+3&#x2F;4+4&#x2F;7+0)&#x2F;5 &#x3D; 0.664</p>
<p>AP(查询二) &#x3D; (1&#x2F;3+2&#x2F;5+3&#x2F;6+4&#x2F;8+0)&#x2F;5 &#x3D; 0.347</p>
<p>这个时候mAP &#x3D; (0.664+0.347)&#x2F;2 &#x3D; 0.51</p>
<p><strong>分析：</strong>对于上面的例子，最好的结果就是5个条目全部被检索到，并且分别排在rank&#x3D;1、2、3、4、5的位置，这时AP&#x3D;1。<strong>所以可以得出即使条目被全部检索到，但结果的先后顺序决定了一个系统的好坏。这个结论会用在目标检测当中。</strong></p>
<p><strong>注：</strong>precision在计算的时候取各个召回率下最大的那个，因为同一recall下最大的precision表示该条目最先出现的位置。</p>
<h3 id="3、目标检测中的mAP"><a href="#3、目标检测中的mAP" class="headerlink" title="3、目标检测中的mAP"></a>3、目标检测中的mAP</h3><p>  图像分类任务通常用accuracy来衡量模型的准确率，对于目标检测任务，比如测试集上的所有图片一共有1000个object（这里的object不是图片的数量，因为一张图片中可能包含若干个object），两个模型都正确检测出了900个object（IOU&gt;规定的阈值）。与图像分类任务不同的是，目标检测因为可能出现重复检测的情况，所以不是一个n to n的问题。在上面的例子中也就不能简单用分类任务的accuracy来衡量模型性能，因为模型A有可能是预测了2000个结果才中了900个，而模型B可能只预测了1200个结果。模型B的性能显然要好于A，因为模型A更像是广撒网，误检测的概率比较高。想象一下如果将模型A用在自动驾驶的汽车上，出现很多误检测的情况对汽车的安全性和舒适性都有很大影响。</p>
<p>  那在目标检测任务中，应该怎样衡量模型的性能？其中一个标准就是信息检索那样，不仅要衡量检测出正确目标的数量，还应该评价模型是否能以较高的precision检测出目标。也就是在某个类别下的检测，在检测出正确目标之前，是不是出现了很多判断失误。AP越高，说明检测失误越少。对于所有类别的AP求平均就得到mAP了。</p>
<h3 id="4、计算方法和相关代码"><a href="#4、计算方法和相关代码" class="headerlink" title="4、计算方法和相关代码"></a>4、计算方法和相关代码</h3><p><strong>voc2007的计算方法：</strong><br>在计算AP时，首先要把结果按照置信度排序，公式如下：<br><img src="/posts/9fc5d2ad/2.png" alt="image"></p>
<p><strong>voc2010的计算方法：</strong><br>  比起07年，10年以后的新方法是取所有真实的recall值，按照07年的方法得到所有recall&#x2F;precision数据点以后，计算recall&#x2F;precision曲线下的面积：</p>
<blockquote>
<p>Compute a version of the measured precision&#x2F;recall curve with precision monotonically decreasing, by setting the precision for recall r to the maximum precision obtained for any recall r′ ≥ r.<br>Compute the AP as the area under this curve by numerical integration. No approximation is involved since the curve is piecewise constant.</p>
</blockquote>
<p><strong>举一个例子具体说明：</strong><br>对于Aeroplane类别，我们有以下输出（BB表示Bounding Box序号，IOU&gt;0.5时GT&#x3D;1）：</p>
<pre class="language-text" data-language="text"><code class="language-text">BB  | confidence | GT
----------------------
BB1 |  0.9       | 1
----------------------
BB2 |  0.9       | 1
----------------------
BB1 |  0.8       | 1
----------------------
BB3 |  0.7       | 0
----------------------
BB4 |  0.7       | 0
----------------------
BB5 |  0.7       | 1
----------------------
BB6 |  0.7       | 0
----------------------
BB7 |  0.7       | 0
----------------------
BB8 |  0.7       | 1
----------------------
BB9 |  0.7       | 1
----------------------</code></pre>
<p>因此，我们有 TP&#x3D;5 (BB1, BB2, BB5, BB8, BB9), FP&#x3D;5 (重复检测到的BB1也算FP)。除了表里检测到的5个GT以外，我们还有2个GT没被检测到，因此: FN &#x3D; 2. 这时我们就可以按照Confidence的顺序给出各处的PR值，如下：</p>
<pre class="language-text" data-language="text"><code class="language-text">rank=1  precision=1.00 and recall=0.14
------------------------------
rank=2  precision=1.00 and recall=0.29
------------------------------
rank=3  precision=0.66 and recall=0.29
------------------------------
rank=4  precision=0.50 and recall=0.29
------------------------------
rank=5  precision=0.40 and recall=0.29
------------------------------
rank=6  precision=0.50 and recall=0.43
------------------------------
rank=7  precision=0.43 and recall=0.43
------------------------------
rank=8  precision=0.38 and recall=0.43
------------------------------
rank=9  precision=0.44 and recall=0.57
------------------------------
rank=10 precision=0.50 and recall=0.71
------------------------------</code></pre>
<p><strong>07年的方法：</strong><br>  我们选取Recall &gt;&#x3D;{ 0, 0.1, …, 1}的11处Percision的最大值：1, 1, 1, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 0, 0。AP &#x3D; 5.5 &#x2F; 11 &#x3D; 0.5</p>
<p><strong>VOC2010及以后的方法：</strong><br>  对于Recall &gt;&#x3D; {0, 0.14, 0.29, 0.43, 0.57, 0.71, 1}，我们选取此时Percision的最大值：1, 1, 1, 0.5, 0.5, 0.5, 0。计算recall&#x2F;precision下的面积：AP &#x3D; (0.14-0)x1 + (0.29-0.14)x1 + (0.43-0.29)x0.5 + (0.57-0.43)x0.5 + (0.71-0.57)x0.5 + (1-0.71)x0 &#x3D; 0.5</p>
<p>计算出每个类别的AP以后，对于所有类别的AP取均值就得到mAP了。</p>
<p>代码:</p>
<pre class="language-python" data-language="python"><code class="language-python"><span class="token comment"># 计算recall, precision和AP</span>
class_recs <span class="token operator">=</span> <span class="token punctuation">&#123;</span><span class="token punctuation">&#125;</span>
    npos <span class="token operator">=</span> <span class="token number">0</span>
    <span class="token keyword">for</span> imagename <span class="token keyword">in</span> imagenames<span class="token punctuation">:</span>
        R <span class="token operator">=</span> <span class="token punctuation">[</span>obj <span class="token keyword">for</span> obj <span class="token keyword">in</span> recs<span class="token punctuation">[</span>imagename<span class="token punctuation">]</span> <span class="token keyword">if</span> obj<span class="token punctuation">[</span><span class="token string">'name'</span><span class="token punctuation">]</span> <span class="token operator">==</span> classname<span class="token punctuation">]</span> 
        bbox <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>x<span class="token punctuation">[</span><span class="token string">'bbox'</span><span class="token punctuation">]</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> R<span class="token punctuation">]</span><span class="token punctuation">)</span>
        difficult <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>x<span class="token punctuation">[</span><span class="token string">'difficult'</span><span class="token punctuation">]</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> R<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">.</span>astype<span class="token punctuation">(</span>np<span class="token punctuation">.</span><span class="token builtin">bool</span><span class="token punctuation">)</span>
        det <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token boolean">False</span><span class="token punctuation">]</span> <span class="token operator">*</span> <span class="token builtin">len</span><span class="token punctuation">(</span>R<span class="token punctuation">)</span> <span class="token comment">#这个值是用来判断是否重复检测的</span>
        npos <span class="token operator">=</span> npos <span class="token operator">+</span> <span class="token builtin">sum</span><span class="token punctuation">(</span><span class="token operator">~</span>difficult<span class="token punctuation">)</span>
        class_recs<span class="token punctuation">[</span>imagename<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">&#123;</span><span class="token string">'bbox'</span><span class="token punctuation">:</span> bbox<span class="token punctuation">,</span>
                                 <span class="token string">'difficult'</span><span class="token punctuation">:</span> difficult<span class="token punctuation">,</span>
                                 <span class="token string">'det'</span><span class="token punctuation">:</span> det<span class="token punctuation">&#125;</span>

    <span class="token comment"># read dets</span>
    detfile <span class="token operator">=</span> detpath<span class="token punctuation">.</span><span class="token builtin">format</span><span class="token punctuation">(</span>classname<span class="token punctuation">)</span>
    <span class="token keyword">with</span> <span class="token builtin">open</span><span class="token punctuation">(</span>detfile<span class="token punctuation">,</span> <span class="token string">'r'</span><span class="token punctuation">)</span> <span class="token keyword">as</span> f<span class="token punctuation">:</span>
        lines <span class="token operator">=</span> f<span class="token punctuation">.</span>readlines<span class="token punctuation">(</span><span class="token punctuation">)</span>

    splitlines <span class="token operator">=</span> <span class="token punctuation">[</span>x<span class="token punctuation">.</span>strip<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span>split<span class="token punctuation">(</span><span class="token string">' '</span><span class="token punctuation">)</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> lines<span class="token punctuation">]</span>
    image_ids <span class="token operator">=</span> <span class="token punctuation">[</span>x<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> splitlines<span class="token punctuation">]</span>
    confidence <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token builtin">float</span><span class="token punctuation">(</span>x<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> splitlines<span class="token punctuation">]</span><span class="token punctuation">)</span>
    BB <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token builtin">float</span><span class="token punctuation">(</span>z<span class="token punctuation">)</span> <span class="token keyword">for</span> z <span class="token keyword">in</span> x<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">:</span><span class="token punctuation">]</span><span class="token punctuation">]</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> splitlines<span class="token punctuation">]</span><span class="token punctuation">)</span>

    <span class="token comment"># sort by confidence</span>
    sorted_ind <span class="token operator">=</span> np<span class="token punctuation">.</span>argsort<span class="token punctuation">(</span><span class="token operator">-</span>confidence<span class="token punctuation">)</span>
    BB <span class="token operator">=</span> BB<span class="token punctuation">[</span>sorted_ind<span class="token punctuation">,</span> <span class="token punctuation">:</span><span class="token punctuation">]</span>
    image_ids <span class="token operator">=</span> <span class="token punctuation">[</span>image_ids<span class="token punctuation">[</span>x<span class="token punctuation">]</span> <span class="token keyword">for</span> x <span class="token keyword">in</span> sorted_ind<span class="token punctuation">]</span>

    <span class="token comment"># go down dets and mark TPs and FPs</span>
    nd <span class="token operator">=</span> <span class="token builtin">len</span><span class="token punctuation">(</span>image_ids<span class="token punctuation">)</span>
    tp <span class="token operator">=</span> np<span class="token punctuation">.</span>zeros<span class="token punctuation">(</span>nd<span class="token punctuation">)</span>
    fp <span class="token operator">=</span> np<span class="token punctuation">.</span>zeros<span class="token punctuation">(</span>nd<span class="token punctuation">)</span>
    <span class="token keyword">for</span> d <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span>nd<span class="token punctuation">)</span><span class="token punctuation">:</span>
        R <span class="token operator">=</span> class_recs<span class="token punctuation">[</span>image_ids<span class="token punctuation">[</span>d<span class="token punctuation">]</span><span class="token punctuation">]</span>
        bb <span class="token operator">=</span> BB<span class="token punctuation">[</span>d<span class="token punctuation">,</span> <span class="token punctuation">:</span><span class="token punctuation">]</span><span class="token punctuation">.</span>astype<span class="token punctuation">(</span><span class="token builtin">float</span><span class="token punctuation">)</span>
        ovmax <span class="token operator">=</span> <span class="token operator">-</span>np<span class="token punctuation">.</span>inf
        BBGT <span class="token operator">=</span> R<span class="token punctuation">[</span><span class="token string">'bbox'</span><span class="token punctuation">]</span><span class="token punctuation">.</span>astype<span class="token punctuation">(</span><span class="token builtin">float</span><span class="token punctuation">)</span>

        <span class="token keyword">if</span> BBGT<span class="token punctuation">.</span>size <span class="token operator">></span> <span class="token number">0</span><span class="token punctuation">:</span>
            <span class="token comment"># compute overlaps</span>
            <span class="token comment"># intersection</span>
            ixmin <span class="token operator">=</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span> bb<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
            iymin <span class="token operator">=</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> bb<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
            ixmax <span class="token operator">=</span> np<span class="token punctuation">.</span>minimum<span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">,</span> bb<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
            iymax <span class="token operator">=</span> np<span class="token punctuation">.</span>minimum<span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">,</span> bb<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
            iw <span class="token operator">=</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>ixmax <span class="token operator">-</span> ixmin <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">)</span>
            ih <span class="token operator">=</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>iymax <span class="token operator">-</span> iymin <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">)</span>
            inters <span class="token operator">=</span> iw <span class="token operator">*</span> ih

            <span class="token comment"># union</span>
            uni <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token punctuation">(</span>bb<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span> <span class="token operator">-</span> bb<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">*</span> <span class="token punctuation">(</span>bb<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span> <span class="token operator">-</span> bb<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">+</span>
                   <span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">]</span> <span class="token operator">-</span> BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">*</span>
                   <span class="token punctuation">(</span>BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token punctuation">]</span> <span class="token operator">-</span> BBGT<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">+</span> <span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">-</span> inters<span class="token punctuation">)</span>

            overlaps <span class="token operator">=</span> inters <span class="token operator">/</span> uni
            ovmax <span class="token operator">=</span> np<span class="token punctuation">.</span><span class="token builtin">max</span><span class="token punctuation">(</span>overlaps<span class="token punctuation">)</span>
            jmax <span class="token operator">=</span> np<span class="token punctuation">.</span>argmax<span class="token punctuation">(</span>overlaps<span class="token punctuation">)</span>

        <span class="token keyword">if</span> ovmax <span class="token operator">></span> ovthresh<span class="token punctuation">:</span>
            <span class="token keyword">if</span> <span class="token keyword">not</span> R<span class="token punctuation">[</span><span class="token string">'difficult'</span><span class="token punctuation">]</span><span class="token punctuation">[</span>jmax<span class="token punctuation">]</span><span class="token punctuation">:</span>
                <span class="token keyword">if</span> <span class="token keyword">not</span> R<span class="token punctuation">[</span><span class="token string">'det'</span><span class="token punctuation">]</span><span class="token punctuation">[</span>jmax<span class="token punctuation">]</span><span class="token punctuation">:</span>
                    tp<span class="token punctuation">[</span>d<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1.</span>
                    R<span class="token punctuation">[</span><span class="token string">'det'</span><span class="token punctuation">]</span><span class="token punctuation">[</span>jmax<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1</span> <span class="token comment">#判断是否重复检测，检测过一次以后，值就从False变为1了</span>
                <span class="token keyword">else</span><span class="token punctuation">:</span>
                    fp<span class="token punctuation">[</span>d<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1.</span>
        <span class="token keyword">else</span><span class="token punctuation">:</span>
            fp<span class="token punctuation">[</span>d<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">1.</span>

    <span class="token comment"># compute precision recall</span>
    fp <span class="token operator">=</span> np<span class="token punctuation">.</span>cumsum<span class="token punctuation">(</span>fp<span class="token punctuation">)</span>
    tp <span class="token operator">=</span> np<span class="token punctuation">.</span>cumsum<span class="token punctuation">(</span>tp<span class="token punctuation">)</span>
    rec <span class="token operator">=</span> tp <span class="token operator">/</span> <span class="token builtin">float</span><span class="token punctuation">(</span>npos<span class="token punctuation">)</span>
    <span class="token comment"># avoid divide by zero in case the first detection matches a difficult</span>
    <span class="token comment"># ground truth</span>
    prec <span class="token operator">=</span> tp <span class="token operator">/</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>tp <span class="token operator">+</span> fp<span class="token punctuation">,</span> np<span class="token punctuation">.</span>finfo<span class="token punctuation">(</span>np<span class="token punctuation">.</span>float64<span class="token punctuation">)</span><span class="token punctuation">.</span>eps<span class="token punctuation">)</span>
    ap <span class="token operator">=</span> voc_ap<span class="token punctuation">(</span>rec<span class="token punctuation">,</span> prec<span class="token punctuation">,</span> use_07_metric<span class="token punctuation">)</span>

    <span class="token keyword">return</span> rec<span class="token punctuation">,</span> prec<span class="token punctuation">,</span> ap</code></pre>

<p>计算AP:</p>
<pre class="language-python" data-language="python"><code class="language-python"><span class="token keyword">def</span> <span class="token function">voc_ap</span><span class="token punctuation">(</span>rec<span class="token punctuation">,</span> prec<span class="token punctuation">,</span> use_07_metric<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">)</span><span class="token punctuation">:</span>
    <span class="token triple-quoted-string string">"""Compute VOC AP given precision and recall. If use_07_metric is true, uses
    the VOC 07 11-point method (default:False).
    """</span>
    <span class="token keyword">if</span> use_07_metric<span class="token punctuation">:</span>
        <span class="token comment"># 11 point metric</span>
        ap <span class="token operator">=</span> <span class="token number">0.</span>
        <span class="token keyword">for</span> t <span class="token keyword">in</span> np<span class="token punctuation">.</span>arange<span class="token punctuation">(</span><span class="token number">0.</span><span class="token punctuation">,</span> <span class="token number">1.1</span><span class="token punctuation">,</span> <span class="token number">0.1</span><span class="token punctuation">)</span><span class="token punctuation">:</span>
            <span class="token keyword">if</span> np<span class="token punctuation">.</span><span class="token builtin">sum</span><span class="token punctuation">(</span>rec <span class="token operator">>=</span> t<span class="token punctuation">)</span> <span class="token operator">==</span> <span class="token number">0</span><span class="token punctuation">:</span>
                p <span class="token operator">=</span> <span class="token number">0</span>
            <span class="token keyword">else</span><span class="token punctuation">:</span>
                p <span class="token operator">=</span> np<span class="token punctuation">.</span><span class="token builtin">max</span><span class="token punctuation">(</span>prec<span class="token punctuation">[</span>rec <span class="token operator">>=</span> t<span class="token punctuation">]</span><span class="token punctuation">)</span>
            ap <span class="token operator">=</span> ap <span class="token operator">+</span> p <span class="token operator">/</span> <span class="token number">11.</span>
    <span class="token keyword">else</span><span class="token punctuation">:</span>
        <span class="token comment"># correct AP calculation</span>
        <span class="token comment"># first append sentinel values at the end</span>
        mrec <span class="token operator">=</span> np<span class="token punctuation">.</span>concatenate<span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token number">0.</span><span class="token punctuation">]</span><span class="token punctuation">,</span> rec<span class="token punctuation">,</span> <span class="token punctuation">[</span><span class="token number">1.</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
        mpre <span class="token operator">=</span> np<span class="token punctuation">.</span>concatenate<span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token number">0.</span><span class="token punctuation">]</span><span class="token punctuation">,</span> prec<span class="token punctuation">,</span> <span class="token punctuation">[</span><span class="token number">0.</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">)</span>

        <span class="token comment"># compute the precision envelope</span>
        <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span>mpre<span class="token punctuation">.</span>size <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">:</span>
            mpre<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> np<span class="token punctuation">.</span>maximum<span class="token punctuation">(</span>mpre<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> mpre<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span>
        i <span class="token operator">=</span> np<span class="token punctuation">.</span>where<span class="token punctuation">(</span>mrec<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">:</span><span class="token punctuation">]</span> <span class="token operator">!=</span> mrec<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span>

        <span class="token comment"># and sum (\Delta recall) * prec</span>
        ap <span class="token operator">=</span> np<span class="token punctuation">.</span><span class="token builtin">sum</span><span class="token punctuation">(</span><span class="token punctuation">(</span>mrec<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">-</span> mrec<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token operator">*</span> mpre<span class="token punctuation">[</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment">#计算面积</span>
    <span class="token keyword">return</span> ap</code></pre>

<p>计算mAP:</p>
<pre class="language-python" data-language="python"><code class="language-python"><span class="token keyword">def</span> <span class="token function">mAP</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">:</span>

    detpath<span class="token punctuation">,</span>annopath<span class="token punctuation">,</span>imagesetfile<span class="token punctuation">,</span>cachedir<span class="token punctuation">,</span>class_path <span class="token operator">=</span> get_dir<span class="token punctuation">(</span><span class="token string">'kitti'</span><span class="token punctuation">)</span>
    ovthresh<span class="token operator">=</span><span class="token number">0.3</span><span class="token punctuation">,</span>
    use_07_metric<span class="token operator">=</span><span class="token boolean">False</span>

    rec <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> prec <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> mAP <span class="token operator">=</span> <span class="token number">0</span>
    class_list <span class="token operator">=</span> get_classlist<span class="token punctuation">(</span>class_path<span class="token punctuation">)</span>
    <span class="token keyword">for</span> classname <span class="token keyword">in</span> class_list<span class="token punctuation">:</span>
        rec<span class="token punctuation">,</span> prec<span class="token punctuation">,</span> ap <span class="token operator">=</span> voc_eval<span class="token punctuation">(</span>detpath<span class="token punctuation">,</span>
                                 annopath<span class="token punctuation">,</span>
                                 imagesetfile<span class="token punctuation">,</span>
                                 classname<span class="token punctuation">,</span>
                                 cachedir<span class="token punctuation">,</span>
                                 ovthresh<span class="token operator">=</span><span class="token number">0.5</span><span class="token punctuation">,</span>
                                 use_07_metric<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">,</span>
                                 kitti<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">)</span>
        <span class="token keyword">print</span><span class="token punctuation">(</span><span class="token string">'on &#123;&#125;, the ap is &#123;&#125;, recall is &#123;&#125;, precision is &#123;&#125;'</span><span class="token punctuation">.</span><span class="token builtin">format</span><span class="token punctuation">(</span>classname<span class="token punctuation">,</span> ap<span class="token punctuation">,</span> rec<span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> prec<span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
        mAP <span class="token operator">+=</span> ap
    mAP <span class="token operator">=</span> <span class="token builtin">float</span><span class="token punctuation">(</span>mAP<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token builtin">len</span><span class="token punctuation">(</span>class_list<span class="token punctuation">)</span>

    <span class="token keyword">return</span> mAP</code></pre>

                
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                            引言：
有时候使用conda安装环境时，遇到较大的包下载极其缓慢，并且在设置好镜像后还是安装缓慢，这里分享一个离线安装的办法。

通过其他方法下载所需要的包1. 通过浏览器下载  在镜像网站中找到需要的安装包的下载地址（或者通过conda安
                        
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